When comparing Telegram vs Pushbullet, the Slant community recommends Pushbullet for most people. In the question“What are the best Material Design apps?”Pushbullet is ranked 2nd while Telegram is ranked 28th. The most important reason people chose Pushbullet is:

Pushbullet also allows its users to push messages, links, files, locations, and more to any of their devices or to other Pushbullet users.

Pros

Pro

Free and convenient large file sharing

Copy/paste videos, gifs, images, geolocation, and documents, drag over files for practically any time up to 1.5GB in size. Images can be compressed, too.

Pro

Privacy focused

In addition to the end-to-end encryption that provides privacy to communications, the app also includes self destructing timers for chats, and the ability to permanently delete messages, yours and theirs, from your device.

Pro

Secure

Telegram uses an open source MTProto encryption protocol that provides complete end-to-end encryption for secret chats. To show off their confidence in the protocol the company behind Telegram has organized $200,000 and $300,000 challenges to break the encryption. So far there have been no winners.

Pro

Beautiful UI

Very customizable with a lot of clean looking options.

Pro

Media messaging

Videos, gifs, images, geolocation, and documents.

Pro

Possible to send photos and videos without compression

Pro

2-step verification

You can set up an additional password to your account, which can be reset by your email. You don't have to use an email if you do not want to. If you lose access to your email or forget your password, you will be able to reset it via text message if your account is over seven days old and will receive it within a week (in case you recover anything before then).

Pro

Channels for one way broadcasting

Broadcasting channels suitable for announcing things.

Pro

Free of cost

The application is available free of cost.

Pro

Customer support is within the app

Although it's volunteer based, but still pretty top-notch if available, which it tends to be.

Pro

Supergroups of up to 5000 people

In Supergroups, anyone along with admins can delete their messages from all sides. A message can be pinned to the top. All of the user's messages can be deleted by an administrator, and they can be banned and reported as well. Supergroups can have a public link (outside of Asia, due to high spam volumes), which is also a username.

Pro

Desktop app handles HIDPI

The desktop app has a built in setting to scale the UI of the app up to 200% which allows for those with 4k monitors/screens to use the app without scaling issues.

Pro

Save time with inline bots and link previews

Unfortunately, on the desktop videos don't play, but images are viewable without visiting popular websites like imgur and Instagram.

You can play YouTube videos and others within the app, so you don't need to embed code or anything.

With inline bots, such as @gif, @pic/bing, @vid/YouTube, etc, you can look things up without leaving the client or chat that you're in. Simply type the name and some keywords and wait for the results to load.

Pro

Cloud chat keys are kept in different jurisdiction

Even though encryption used for cloud-based storage (e.g. Gmail, Facebook, iCloud) may not be as secure as end-to-end encryption or zero-knowledge storage, Telegram does the most that it can by holding keys to chats in different jurisdictions, requiring intergovernmental cooperation to obtain the keys. This is aside from whatever other security measures have been taken, of course.

Pro

High quality calls

Uses the latest GPL audio codecs, such as Opus, an adaptative high-quality codec that supersedes AAC at any bitrate.

Pro

Does a lot more than just notifications

Pushbullet also allows its users to push messages, links, files, locations, and more to any of their devices or to other Pushbullet users.

Pro

Superbly easy to use

After installing the Pushbullet application the set up process is as easy as it gets. Pushbullet will first ask you to sign in to your Google account. Then all you have to do is enable notification access and install the Chrome extension.

Pro

Almost no delay

Pushbullet is just as fast as its name suggests at mirroring notifications or pushing links or files.

Pro

Free

Pushbullet is free with no advertisements.

Pro

Chrome notifications act as a notification drawer

Pushbullet uses Chrome notifications to act as a running list of past notification that have not yet been dismissed. This is especially useful if you receive a lot of notifications or you are not at your computer when they are received.

Pro

Uses a Chrome extension for PC/Mac or a Windows application

Pushbullet is designed to use its Chrome extension although a Windows application can be used as well. The Chrome extension provides the best experience because any computer with a signed in Chrome browser will provide your Android notifications.

Pro

Cross device notification mirroring

Pushbullet can even sync notifcations with other Android devices (beta). This helps prevent you from having to dismiss notifications more than once and allows you to always see your notifications no matter what device you're on.

Pro

Runs without Chrome open

As long as you enable "Keep Pushbullet running after I close Chrome" in the Pushbullet extension options, Chrome does not need to be open to receive notifications.

Pro

More information shown in the notification than other services

Pushbullet includes the sender's name, email address, unread count, subject, and a preview of the message all in the notification.

Pro

Universal Copy/Paste

Copy text on PC,paste it on your Android device and vice versa. You need the windows app for this. iOS and OSX support coming soon.

Cons

Con

Not fully open source

Telegram has an open API and protocol free for everyone, but the backend software is not open source. Therefore 100% privacy can not be evaluated.

Con

Only "Secret Chat" messages are encrypted end to end

The only way to get end-to-end encryption (client-client) using Telegram is to use the Secret Chat function, anything through the service is server-client encrypted. Also secret chat is only implemented in the mobile apps, meaning there is no way to encrypt messages end-to-end when using the desktop client or the web browser client.

Con

Can only be used with a phone number.

It is not possible to activate and use Telegram by mail etc. You need a phone number.

Con

Mac users must use their browser

There is currently no desktop application for Mac users available. The Pushbullet website claims a native OSX client is "coming soon".